For the shrimp: Heat a large skillet over medium-high heat. Add the vegetable oil, sausage and shrimp. Cook for 1 minute, and then turn the shrimp over and continue cooking. Add the garlic and rosemary sprig and cook for another minute.
Pour in the wine to deglaze, and then add the butter and 1/2 teaspoon of the BBQ seasoning. Reduce the heat to medium and swirl the pan to incorporate the butter. Taste and add 1/2 teaspoon more of the seasoning, if needed. Reserve the remaining seasoning in an airtight container for another use.
Transfer the shrimp and sausage to a serving bowl and garnish with a slice of grilled Tuscan bread.